### Treatment of phenotypic data

All analyses used the simulated data on 1000 offspring from 20 dams, nested in 5 sire families. Univariate analyses in ASREML [1] were used to estimate heritabilities at each of the time points. The Gompertz growth function, modelling weight over time, was fitted across all trait data using nonlinear regression in SAS. The following parameterization of the Gompertz equation was used: y(t) = Ae^{{-e[Be(C-t)/A]}} , where:

y(t) = yield at time t; A = final yield; B = maximum growth rate; C = age at maximum growth rate.

The Gompertz function was then fitted to trait information for each individual separately and individual estimates of the model parameters A, B, C were extracted. Subsequently, parameter estimates for each individual were employed in the model equation and its derivative to predict yield and growth rate (yield per day), respectively, at the 5 time points for which trait information was available (0 to 530) and at time 600.

### Variance component QTL analyses

A variance component approach was used to look for additive, dominant and imprinted QTL. Following a two-step approach [4], identical-by-descent (IBD) coefficients were estimated for all relationships in the pedigree with the recursive method of Pong-Wong *et al,*[5]. Variance components for each model were estimated using ASReml [1]. The following models were evaluated

(1) **y** = **Xβ** + **Zu** + **e**(null or polygenic)

(2) **y** = **Xβ** + **Zu** + **Za** + **e**(additive QTL)

(3) **y** = **Xβ** + **Zu** + **Za** + **Zd** + **e** (additive QTL + dominant QTL)

(4) **y** = **Xβ** + **Zu** + **Z**_{
m
}**m** + **Z**_{
p
}**p** + **e** (maternal QTL + paternal QTL)

where **y** is a vector of phenotypic observations, **β** is a vector of fixed effects, **u, a, d, m, p** and **e** are vectors of random additive polygenic effects, additive and dominance QTL effects, maternal and paternal QTL effects and residuals, respectively. **X, Z, W, Zm,** and **Zp** are incidence matrices relating to fixed and random genetic, maternally expressed, and paternally expressed QTL effects, respectively. Variances for polygenic and QTL effects are distributed as follows: var**(u)** =**A**σ^{2}_{a}, Var**(a)** = **G**σ^{2}_{q}, Var**(d)** = **D**σ^{2}_{d}, Var**(m)** = **G**_{
M
}σ^{2}_{m}, Var**(p)** = **G**_{
P
}σ^{2}_{p}, var**(e)** = **I**σ^{2}_{e}. **A** is the standard additive relationship matrix based on pedigree data only and the relationship matrices. The **G, G**_{
M
}**, G**_{
P
} and **D** are the appropriate relationship matrices used to model the additive, maternal, paternal and dominant QTL effects at each position tested as outlined by Liu *et al,*[6].

The logarithm of the likelihood ratio test statistic was used to test the presence of a QTL at given locations along the genome. A nominal χ^{2}_{1} or χ^{2}_{2} was used depending on whether one or two extra parameters were estimated. This has been shown to be conservative as the theoretical distribution is a mixture between 0 and χ^{2}_{1} or χ^{2}_{1} and χ^{2}_{2}, respectively[7].

Models (3) vs. (2) were compared to detect dominant effects. Models (4) vs. (1) were compared to test for an additive QTL whilst allowing the maternal and paternal components to vary and (4) vs (2) to test whether the additive effect was better explained by allowing different parental contributions.

### Association studies

We first tested the level of linkage disequilibrium (LD) using Haploview [8]. For association analyses, we used the simulated phenotypes as well as the Gompertz parameters A, B, C (results not shown). Association analyses were performed using the GRAMMAR approach [10], which comprises two stages. First, ASReml is used to correct each phenotype for polygenic effects; and second, additive, dominant and imprinting models were sequentially fitted against each marker on the residual phenotypic values with an ANOVA test. In the case of a better fit of the imprinting model for a given SNP, we generated a 5% significance level by performing 2000 randomizations where we randomly swapped the maternal and paternal allelic origin for half the offspring. An empirical genome-wide threshold of 5% was generated from 1,000 permutations. We also applied haplotype analyses and exhaustive epistatic searches, but these revealed no additional QTL.